German chancellor and French president act to ease fears that Spain's economic woes could threaten European single currency

German chancellor Angela Merkel with French president François Hollande in Berlin this year. The pair said in a joint statement that their countries are 'deeply committed to the integrity of the eurozone'. Photograph: Markus Schreiber/AP

Angela Merkel and François Hollande on Friday pledged a joint determination to save the euro as they sought to quash fears in the world's financial markets that the deepening economic woes of Spain would put the single currency at risk.

The show of support from the German chancellor and the French president helped extend the rally on Europe's financial markets into a second day and was enough to divert attention from dismal Spanish unemployment figures and a warning from the International Monetary Fund that Spain's deepening crisis posed a threat to monetary union.

Spain's borrowing costs for its 10-year bonds dropped to 6.76% – a percentage point drop on the levels seen earlier in the week – while the Ibex index of shares in Madrid closed more than 3% higher.

In Rome, where the Italian government extended its ban on the short selling of shares – the process whereby investors sell stocks they do not own in the hope of buying them back more cheaply later, the FTSE MIB rose by 3%.

On the foreign exchanges the euro climbed to almost €1.24 against the US dollar. Share prices in London and New York also gained ground.

"France and Germany are fundamentally tied to the integrity of the euro area," Merkel and Hollande said in their statement after a telephone call between the two leaders. "They are determined to do everything to protect it. Member states and European institutions must fulfil their obligations to this end, according to their prerogatives."

With the German Bundesbank again warning the European Central Bank against exceeding its mandate in an attempt to help beleaguered eurozone countries, there was confusion in the markets as to when and how the verbal show of support for Spain would be put into action.

The government in Madrid strongly denied a report from Reuters that a meeting in Berlin on Tuesday between the German finance minister, Wolfgang Schäuble, and his Spanish counterpart, Luis de Guindos, had discussed a €300bn (£236bn) package of financial support.

In its annual Article 4 health check, the IMF predicted it would take until 2017 for national output to return to its 2007 level, before the global financial crisis hit.

It said: "Spain is facing mounting market pressure and costly market access, with possibly negative repercussions for the rest of Europe, amid the longer term challenge of unwinding imbalances that built up during several years of excess private sector spending."

Official figures released in Madrid on Friday showed that Spain's unemployment rate hit record levels in the second quarter of this year, leaving one in four of the working population without a job as austerity continued to bite and fears of a national bailout grew.

Figures released by the country's national statistics institute revealed that the second quarter, traditionally a time when employment picks up for the tourism season, saw joblessness rise to 24.6% as 53,000 more people joined dole queues. That broke a record set during Spain's last major recession 18 years ago.

More than 5.7 million Spaniards are unemployed.

The under-25s are suffering most, with 53% of jobseekers unable to find work.

One in three people are now jobless in the Canary Islands and across a whole swath of western and southern Spain covering the regions of Extremadura and Andalucia.